Carbon pricing and planetary boundaries

(1)

Gustav Engström ^1,2✉, Johan Gars^1,2, Chandra Krishnamurthy^1,3, Daniel Spiro⁴, Raphael Calel ⁵, Therese Lindahl ^1,6& Badri Narayanan ⁷

Human activities are threatening to push the Earth system beyond its planetary boundaries, risking catastrophic and irreversible global environmental change. Action is urgently needed, yet well-intentioned policies designed to reduce pressure on a single boundary can lead, through economic linkages, to aggravation of other pressures. In particular, the potential policy spillovers from an increase in the global carbon price onto other critical Earth system processes has received little attention to date. To this end, we explore the global environmental effects of pricing carbon, beyond its effect on carbon emissions. Weﬁnd that the case for carbon pricing globally becomes even stronger in a multi-boundary world, since it can ameliorate many other planetary pressures. It does however exacerbate certain planetary pressures, largely by stimulating additional biofuel production. When carbon pricing is allied with a biofuel policy, however, it can alleviate all planetary pressures.

https://doi.org/10.1038/s41467-020-18342-7 OPEN

1Beijer Institute of Ecological Economics, Royal Swedish Academy of Sciences, 10405 Stockholm, Sweden.²GEDB, Royal Swedish Academy of Sciences, 10405 Stockholm, Sweden.³Swedish University of Agricultural Sciences (SLU), 90187 Umeå, Sweden.⁴Department of Economics, Uppsala University, 751 20 Uppsala, Sweden.⁵Georgetown University, Washington, DC 20057, USA.⁶Stockholm Resilience Centre, Stockholm University, 10691

Stockholm, Sweden.⁷School of Environmental and Forestry Sciences, University of Washington Seattle, Seattle, WA 98074, USA. ✉email:gustav.

engstrom@beijer.kva.se

1234567890():,;

(2)

The Earth has been in a remarkably steady state over the last 10,000 years, but human activities since the industrial revolution are now starting to threaten its balance. Rock- ström and colleagues^1,2have developed a list of nine Earth system processes (ESPs) that are critical to maintaining a stable global environment: biogeochemical ﬂows, ocean acidiﬁcation, freshwater use, land-use change, biodiversity loss, atmospheric aerosol loading, ozone depletion, and chemical pollution. There are also nine corresponding planetary boundaries beyond which mankind may not proceed without risking potentially catastrophic consequences^2,3. Even as these planetary boundaries are gaining policy recognition^4,5, the complexity of the many interlocking processes can seem to present decision makers with an unna- vigable obstacle course.

In this paper, we develop a stylized yet empirically grounded framework for analyzing these interlocking processes. We assess the environmental consequences of a global carbon pricing policy in a multi-boundary world^2,3. While it seems unlikely that a global carbon price would be adopted in the near term, this policy serves as a useful proxy for more stringent climate policy in general. Consequently, our analysis may be interpreted as identifying which ESPs are of particular concern when (if) climate policy becomes more ambitious. Carbon pricing is frequently viewed as a matter of applying the brakes on greenhouse gas emissions, but a multi-boundary perspective alerts us to the possibility that it might inadvertently redirect economic activities in ways that exacerbate (or alleviate) other harmful environmental pressures. For instance, a carbon tax targeting fossil fuels will most likely stimulate the production of biofuels, such as palm oils, leading to both additional land-conversion and adverse effects on biodiversity^6,7. Consequently, a speciﬁc policy that moves the Earth system away from one boundary could inadvertently move it toward another⁸. A better analogy to the problem of policy-making with multiple planetary boundaries may, therefore, be that of parallel parking, where the challenge is to simultaneously respect boundaries on all sides, ensuring a safe operating space for global societal development³.

Prior literature has mainly focused on studying how policies affect a single ESP in isolation^9,10, or on developing large-scale computational models to provide counterfactual simulations for two closely related ESPs, such as land-use/deforestation, or climate change/food security^11–14. The purpose of the present paper differs from these in at least two important aspects. First, the scope of our analysis involves all planetary boundaries and encompasses a majority of the underlying drivers. Second, our intentions are to provide a framework that is rich enough to let researchers investigate and discover the complex ways in which policies can interact with multiple ESPs, while also being simple enough to yield a qualitative understanding of the intended and unintended side effects of global environmental policies. Our objective is thus to establish a high-level understanding of how economic markets drive and interact with the planetary boundaries.

To this end, we present a new global economic policy analysis model developed speciﬁcally for the analysis of the economic drivers threatening the safe operating space for global societal development. The model includes the quantitatively most important economic drivers of environmental change, is cali- brated using data from one of the most widely-used sources for economic modeling, the Global Trade Analysis Project (GTAP)¹⁵, and links these economic sectors to the ESPs highlighted in the planetary boundaries framework. We focus exclusively on economic linkages and for the sake of transparency, thus exclude from any direct linkages between biophysical processes which has previously been assessed in e.g. ref. ¹⁶. The model is further designed to both enable replication and independent assessment

of presented ﬁndings (attempting to address the transparency concerns often directed at large-scale IAMs^17,18), as well as further exploration of the effects of other policies on multiple planetary boundaries.

Our analysis reveals that global carbon pricing, deﬁned as a fee, tax, or restriction imposed on the burning of carbon-based fossil fuel sources, including coal, oil and gas (effectively raising the price on fossil fuels), can relieve pressure on all ESPs except land use and freshwater. Although a global carbon price is unlikely to be adopted, several national examples do exist¹⁹. Recent studies also suggest that a carbon price if combined with revenue recy- cling could receive public support²⁰. We also consider the effect of reducing current subsidies for biofuel production as a complementary policy. Such a policy has at times been suggested²¹ and is, in fact, implied by the EU Energy Directive that seeks to limit biofuel usage from food and feed crops. We ﬁnd that the combination of carbon pricing and reduction in biofuel subsidies appears able to ease all of the planetary pressures.

To summarize, the case for a global carbon price appears to be even stronger in a multi-boundary world than when considering climate change as an isolated problem. Caution is however, warranted since higher carbon prices tend to make biofuel production more competitive, which implies that auxiliary policies will be needed in order to reduce all of the key planetary pressures outlined in refs.^2,3.

Results

Economic drivers of planetary pressures. The planetary boundaries can be viewed as a list of the greatest global environmental problems caused by and facing mankind. Since these environmental problems are driven by economic activities, the first step in understanding the nature of the problem is to identify the principal sources of anthropogenic pressure on each ESP, and the links between them. Supplementary Table 1 summarises how specific activities in different economic sectors affect each ESP in the planetary boundaries framework, based on a review of the literature. It should be noted that our interpretations of the boundaries mostly follows³, with the exceptions of the biosphere integrity and novel entity boundaries. These boundaries were replaced by the previous definitions, biodiversity loss, and chemical pollution found², as this greatly reduced the ambiguity in identifying the sources of pressure.

As is evident from Supplementary Table 1, and previously pointed out in e.g. refs. ^22,23, the agricultural sector creates a substantial source of pressure on the ESPs. Hence, despite agricultural activity accounting for merely 4% of global economic output²⁴, it uses a very large share of the planets natural resources. About 40% of the Earth’s land surface is used for agriculture, and it is still the primary driver of land conversion. It also contributes to roughly a quarter of global greenhouse gas emissions and accounts for over 90% of global freshwater, phosphorus, and nitrogen use. Agriculture is thus a primary driver of freshwater over-consumption and biogeochemical loading. Apart from the agricultural sector, fossil fuel consumption is also a key source of pressure on several ESPs. This is due partly to its direct impact on climate change, aerosol loading and ocean acidiﬁcation and partly due to the pressure exerted on other ESPs indirectly through economic channels. For example, biogeochemical ﬂows are highly dependent on fossil fuels. It is thus evident that both agriculture and fossil fuel consumption, as well as their interaction, are vital components of any model that aims to capture how human activity exerts pressure on the ESPs.

Further details and references which motivate the choice of economic sectors included in our model are provided in Supplementary Note 1.

(3)

Model description. In order to systematically study the combined effects of economic linkages between the ESPs, we develop a model of the global economy with a focus on the key economic drivers of planetary pressure. Having a coherent economic framework that links the different ESPs via markets allows us to investigate whether a policy enacted in one domain is likely to create serious risks due to an increasing pressure imposed on other ESPs. We follow standard practice in economic modeling by characterizing a decentralized market structure, with a mul- titude of economic actors who maximize their individual objectives, resulting in competition for a limited set of resources, where the resulting allocation is often referred to as a competitive equilibrium. The model has many elements in common with integrated assessment models (IAMs), such as the DICE¹⁰ or IMAGE²⁵models, but also differs in many aspects, such as degree of detail, aggregation and solution approach adopted, primarily as a result of being intentionally developed to answer our speciﬁc research question.

Figure1provides a schematic outline of the model. Guided by the ﬁndings discussed in Supplementary Note 1, our model characterizes production choices in the following key economic sectors: agriculture, biofuels, timber production, fertilizer production, phosphate extraction, water extraction, manufacturing, energy services, fossil-fuel production, renewable energy (other than biofuels) and ﬁsheries. In total, these sectors account for more than 90% of the drivers for the majority of the planetary pressures (see Supplementary Table 1 for a summary and Supplementary Note 1 for a detailed discussion). Many of the

sectors are economically linked, which allows for an evaluation of many critical trade-offs, for instance, the allocation of land across agriculture and timber production (as in ref.²⁶) or of agricultural output, which can be used as either food or biofuel (similar to ref. ²⁷). The model details are outlined in the “Methods” and Supplementary Methods section.

Two broad features of our modeling approach are however, worth highlighting. First, we approach computations via a method known as comparative statics, an approach that can be characterized as an analysis of the effects of exogenous policy changes using a linear approximation around the equilibrium outcome. Interventions like taxes and quotas can thus be represented as perturbations to the equilibrium, making it easy to trace out their propagation through the entire economy. The effects on the planetary pressures are computed as the net effects of the policy-induced changes in the various economic activities.

Apart from increased transparency, this approach also has the advantage that the model parameters are easier to interpret (for instance, instead of more abstract production function parameters, the model uses shares of total input expenditures in a sector that goes to a speciﬁc input). In total, three sets of parameter estimates need to be assessed, elasticities (demand, supply, and substitution), expenditure shares of the economic sectors andﬁnally quantity shares (see “Methods”).

Second, our focus is on providing a qualitative understanding of the central processes and interactions involved. Hence, our modeling framework does not at present incorporate dynamic aspects of the problem. The model also does not include

Consumption goods Manufact. goods, Land,

Timber

Food Agricultural goods

Fish

Manufacturing Energy services

Energy services Fossil fuels, Biofuels

Renewables

Fertilizers Fossil fuel, Phosphate

Agriculture Land, Fertilizers, Energy

Services, Freshwater Fossil fuels

Freshwater

Phosphate

Fisheries Fossil fuel

Timber Land

Climate change Atmospheric CO2

Ocean acidification Atmospheric CO2

Biodiversity Overexploit., Agriculture

Biogeochemical flows Nitrogen, Phosphorus

Land system change Deforestation

Freshwater Over consumption

Chemical pollution Ozone depletion

Aerosol loading Renewables

Viewer does not support full SVG 1.1

Fig. 1 Schematic of the integrated economic-planetary boundaries model. The above schematic gives an overview of the direct links existing in the model.

The model is built in three layers (columns): consumption, production, and ESPs. The arrows indicate the direction of the economic inputs and outputs and which planetary processes they have an impact on. With the exception of ozone depletion and chemical pollution the impact of the two policy scenarios we consider are quantitatively assessed.

(4)

feedbacks from the planetary pressures to the economy and human welfare. These feedbacks, although important, are unfortunately not understood nearly well enough to inform this kind of modeling exercise, and are thus left for future research.

In summary, our analysis is intended to capture the effects of changes in the economic environment in the short- to medium- term (perhaps 5–10 years). A longer-term analysis would need to take additional aspects, such as technological change and dynamic feedback already referred to, into account. One should be careful, therefore, in applying the framework developed here to long-run decision problems where dynamic feedbacks are likely to be important.

Model parameterization. Among the three broad set of parameter estimates described above, the majority of the estimates needed, can be expressed in terms of expenditure and quantity shares of goods going to different uses (see“Methods”). Detailed sectoral databases, such as the one underlying the widely-used GTAP model¹⁵, allow us to derive a set of internally consistent parameter values. Our model’s 39 parameters are a mix of expenditure shares, quantity shares, and elasticities, with the elasticities chosen to match empirical studies and the shares derived using data from the GTAP database. A complete list of parameters and their sources can be found in the “Methods”, under the Expenditure shares section.

Global carbon pricing. We now consider the policy experiment of a marginal increase in the global carbon price and study its effect on the equilibrium outcome. In the model, the policy is implemented as a tax on fossil fuels (a carbon tax). The analysis would, however, be equivalent for any other policy involving pricing emissions from fossil fuels (e.g., a cap-and-trade system).

As described above, the effects of a policy that increases the carbon price is calculated using a linear approximation around the equilibrium outcome and the derived numbers can be interpreted as percentage changes in response to a one percentage point change in the carbon price. Hence, it should be noted that results from larger perturbations should be interpreted based on the extent to which one can assume that a linear approximation constitutes a reasonable proxy for the true effect.

The direct effect of imposing this increase in the tax rate on fossil fuel use is clearly to increase its (after tax) price leading to a reduction in its demand. Our analysis shows that a one percentage point increase in the global carbon tax rate would reduce annual global CO2 emissions by 0.25% (equivalent to 0.11 GtCO2yr⁻¹), and emissions from fossil fuels by 0.36% (see Supplementary Table 2). The implied elasticity of emission reductions is smaller than in some model-based analyses but is relatively well-aligned with empirical estimates (see Supplementary Note 2).

This reduction in emissions ameliorates pressure on both climate change and ocean acidiﬁcation (depicted as arrows at the top and bottom of Fig.2, pointing inward toward the safe operating space).

This change does not come from a single sector, but rather is the net effect of changes in fossil fuel use in the production of energy services, fertilizer, land use change, etc. Carbon dioxide emissions from fossil fuel use decrease in most sectors as a result of the tax, while emissions from land use change increase due to substitution toward land in agriculture and increased biofuel production. Similar direct impacts occur with aerosol loading. The net effect is a reduction in aerosol loading (measured in terms of aerosol optical depth) following a reduction in the release of atmospheric particles from fossil-fuel burning.

As producers and consumers of fossil fuel react to changing prices, second-order effects arise. To start with, an increase in the carbon tax increases the cost of the nitrogen component of

fertilizers, since nitrogenfixing uses a very fossil-fuel intensive industrial process. Since nitrogen has a high degree of complementarity with phosphate in the production of fertilizers (most fertilizers are sold as multi-nutrient mix- tures), demand for phosphate also decreases, reducing the overall pressure on biogeochemical flows. Furthermore, a carbon tax turns out to reduce pressure on our measure of biodiversity. This is partially due to reduced activity in key sectors such as agriculture andfisheries, in which fossil fuel is an important input. The total effect on biodiversity is the net result of a number of different effects, some positive others negative (see “Numerical results” in “Methods”, for details).

Chemical pollution and stratospheric ozone depletion are only qualitatively assessed based on their relationship to the model variables. If all related model variables move in a direction that decreases the pressure, we draw the conclusion that the net effect is reduced pressure. This turns out to be the case for chemical pollution. For stratospheric ozone depletion, however, the effects go in different directions and we cannot determine the net direction.

A carbon tax will also increase the pressure on land-system change, a net result of several opposing effects. First, a higher relative price of non-land inputs (energy and fertilizer) will encourage substitution toward greater land use in the agricultural sector. At the same time, the higher price of fossil fuel raises the relative price of manufacturing goods compared to e.g., timber and recreation. The demand for non-agricultural uses of land thus counteracts the increase in demand from agriculture. Together with land conversion costs, this results in a small overall increase in land use in the agricultural and timber sectors, which comes at the expense of natural land.

Finally, a carbon tax leads to a small increase in freshwater use.

In this case, the increased freshwater use is primarily due to substitution away from more expensive agricultural inputs. The effect of the carbon tax upon freshwater use illustrates the implications of global aggregation in modeling, i.e., our global aggregate model responds with increased aggregate water use.

In reality, with not all farms across the world being able to substitute freshwater for energy-intensive inputs (e.g., in subsistence farming with no irrigation), other inputs or output must adjust. If freshwater use is constrained in this way, a carbon tax may end up driving down output, or encourage greater substitution along other margins that might exacerbate other planetary pressures.

It is evident that direct effects (on climate change and ocean acidification) are significantly larger than the indirect. The effect on nitrogen use, which is smaller but of similar magnitude to that of climate change, is close to direct, since fossil fuel is an important input in its production. The remaining effects are more indirect and they are an order of magnitude smaller. However, if we were to scale up the effects to the size of the carbon tax required to meet climate policy targets, these smaller indirect effects would be significant.

An increase in the global carbon tax thus reduces pressure on many ESPs besides climate change. The argument for a carbon tax is typically made considering only climate change. Our analysis suggests that in a richer framework, that considers multiple planetary boundaries, the case for a carbon tax is in some ways even stronger. This richer model, however, also alerts us to certain risks, and next, we thus investigate whether a complementary biofuel policy could avert these dangers and move us moreﬁrmly toward the safe operating space.

Reduction of biofuel subsidies. A global carbon tax exerts pressure on the land-system and freshwater ESPs mainly because

(5)

it increases the demand for agricultural output. Delving deeper into the sectoral linkages, one can see that this is not chieﬂy driven by demand for food, but rather demand for biofuels (which is a substitute for fossil fuel). This suggests, that in order to ease the remaining planetary pressures, we need to comple- ment the carbon tax with some additional policy limiting the demand for biofuels.

We thus consider the effect of a complementary reduction of biofuel subsidies (implemented as an increase in a biofuel tax).

Biofuel production is currently heavily subsidised in large parts of the world²⁸. The question is whether it would be prudent to scale back these subsidies in a world with a higher carbon tax. Fig. 3 summarizes the net changes in our model resulting from this two- pronged policy: a one percentage point increase in the carbon tax rate and a one percentage point reduction of the subsidy rate for biofuels.

As is evident from thefigure, this combination of policies can ameliorate pressures on all the ESPs. Biofuel production has not only a negative climate-related effect from increased land use, but also a negative effect on both biogeochemical flows and freshwater systems due to the increased demand for fertilizer and freshwater. Similar results have also been found by ref.²⁹in an assessment of the consequences of a large-scale deployment of bioenergy with carbon capture and storage as a measure for mitigating climate change. Importantly, this result does not necessarily imply that a biofuels subsidy is a bad idea in the absence of a carbon tax. Such a policy would reduce some pressures while increasing others. This analysis assumes biofuels are produced using the same inputs as food and feed, reflecting current production patterns (with biofuel

production using between 1 and 3% of total cropland area, see ref. ²¹). When biofuels of this type are phased out in favor of those not competing directly with food crops for land, either by policy (as required by a new EU Renewable Directive) or technology change (so-called second-generation biofuels), then biofuels may be considered instead as one among other renewable energy sources like solar and wind power.

Sensitivity analysis. To assess the degree to which our ﬁndings are sensitive to parameter choices, we identify key parameters regarding which uncertainty is greater, and choose a range within which they vary. We then solve the model for all possible com- binations of the lower and upper bounds for these parameters, recording the maximum and minimum predicted changes for all model variables.

When a carbon tax is the only policy considered, the signs of the changes in planetary pressures are mostly unaffected, though there are a few notable sign changes. In some extreme scenarios, land use in agriculture and freshwater use may both decrease, and in rare cases, we also observe an increase in phosphate use.

Overall, our sensitivity analysis suggests that, if anything, the outcome distribution tends to be skewed toward reduced rather than increased planetary pressures.

When we supplement the carbon tax with a complementary biofuel subsidy reduction, our results are not as sensitive. There is no reversal in the sign of the net effects. The only change of any relevance for our analysis is that we ﬁnd an increase in food production from agriculture. The details of the sensitivity analysis are reported in Supplementary Table 2.

Biodiversity –0.01% less threats to endangered species

Land-system change +0.01% / +0.5 Mha loss of natural forests

Freshwater use +0.009% / +0.24 km³ yr^–1

Phosphorus –0.01% / –0.9 Gg P yr^–1

Climate change –0.25% / –0.11 GtCO₂ yr^–1

Nitrogen

–0.13% / –0.2 Tg P yr^–1

Ocean acidification –0.25% / –0.11 GtCO₂ yr^–1

Atmospheric aerosol loading

–0.014% / –0.006 mAOD Stratospheric ozone depletion (undecided) Chemical

pollution

Biogeochemical flows

Fig. 2 Changes in planetary pressures resulting from a one percentage point increase in the carbon tax. Thisfigure is a modification of the original planetary boundaryfigure from refs.^1,3. The colors indicate the current state for each boundary: green, yellow, and red correspond to safe, increasing risk and high risk, respectively. We have added arrows illustrating the effects on each individual ESP, from increasing the carbon tax rate by one percentage point in our integrated model of the global economy and the ESPs. The direction of the arrows indicate increasing or decreasing pressure, while the width of the arrows are indicative of the magnitude of change. For chemical pollution and stratospheric ozone depletion, we only derived the qualitative direction of change. Further details are given in Supplementary Table 2.

(6)

Discussion

Carbon pricing is typically justified purely on the basis that it helps mitigate climate change. The planetary boundaries framework developed by Rockström and colleagues¹begs the question as to whether carbon pricing could have unintended side effects, stabilizing or destabilizing, other environmental processes. Here we present an integrated analysis showing that a higher global carbon price may be sufficient to single-handedly reduce almost all planetary pressures. Some of the effects are direct and easy to anticipate, since fossil fuel consumption exerts an important pressure on several ESPs, including climate change and ocean acidification. Other consequences are more indirect, such as a reduction in nutrient-loading, which derives from the importance of fossil fuels in nitrogen production and complementarity between phosphate and nitrogen in fertilizer production. Our analysis shows that, while these indirect effects are significantly smaller than the direct effects, they are still far from insignificant.

A carbon price can also indirectly increase other planetary pressures, especially through increased demand for agricultural land resulting from the increased biofuel demand due to higher fossil fuel prices. We show that a complementary policy of scaling back biofuel subsidies as the carbon price is increased would help avoid these negative effects. This combination of policies provides a means of reducing all planetary pressures.

When interpreting these results, it is however important to bear in mind that we do not make an assessment of the welfare consequences of these changes, meaning that the relative size of the effects need not translate directly to the relative magnitude of resulting welfare effects. Further, while we considered two speciﬁc policies in this paper, the model can very easily be adapted to study the effects of a wide variety of policies. For future research,

we anticipate extending the framework developed here in many directions, accommodating aspects such as dynamics, uncertainty, and welfare analyses.

To summarize, our results suggest that carbon pricing in combination with a reduction in biofuel subsidies can alleviate all key planetary pressures outlined in the planetary boundary framework, suggesting that the case for a global carbon price appears even stronger in a multi-boundary world than when considering climate change in isolation.

Methods

Model components. The results of this paper are derived from a model that is built around the economic sectors outlined as the most important drivers of planetary pressures in Supplementary Table 1. This includes production sectors that have an important direct effect on the ESPs or that have important links to such sectors. They may be linked by using output from such sectors as inputs, providing inputs to such sectors, competing for inputs with such sectors or providing outputs that serve as substitutes for the output from those sectors. The resulting set of included production sectors are: agriculture (producing food and biofuel), energy services, fossil-fuel extraction, renewable energy (other than biofuel), fertilizer production, phosphate extraction, water supply,ﬁsheries, and industrial manufacturing. The demand forﬁnal consumption goods is derived from the maximization of households’ utility. Since we have economic policies in the model, we are implicitly assuming some government entity that imposes these policies, but since we consider the policies exogenous (not, e.g., determined to optimize some objective) we do not explicitly model the government.

We solve the model as a competitive equilibrium where we assume that all agents maximize their respective objectives while taking prices as given (prices are given from the perspective of the individual agent, but are endogenously determined by aggregate supply and demand). We then analyze changes in the endogenously determined model variables in response to an assumed exogenous change in economic policy.

In the model, competition for resources thus leads to a number of important trade-offs. These arise from three main sources including, alternative uses of the output of a sector (e.g., output from the agricultural sector can be used as food or Biodiversity

–0.02% less threats to endangered species

Land-system change –0.04% / –1.5 Mha loss of natural forests

Freshwater use –0.036% / –0.93 km³ yr^–1

Phosphorus –0.05% / –7 Gg P yr^–1

Climate change –0.26% / –0.12 GtCO₂ yr^–1

Nitrogen

–0.18% / –0.3 Tg P yr^–1

Ocean acidification –0.26% / –0.11 GtCO₂ yr^–1

Atmospheric aerosol loading

–0.014% / –0.006 mAOD Stratospheric ozone depletion Chemical

pollution

Biogeochemical flows

Fig. 3 Change in planetary pressures resulting from a one percentage point increase in the tax on carbon and a one percentage point reduction of biofuel subsidies. Thisfigure is a modification of the original planetary boundary figure from refs.^1,3. The colors indicate the current state for each boundary: green, yellow, and red correspond to safe, increasing risk and high risk, respectively. We have added arrows illustrating the effects on each individual ESP, from increasing the tax rate on carbon by one percentage point and reducing biofuel subsidies by one percentage point in our integrated model of the global economy and the ESPs. Interpretation is otherwise the same as in Fig.2. Further details are given in Supplementary Table 3.

(7)

biofuels), sectors competing for the use of inputs (e.g., land can be used for agriculture, forestry or maintained as undisturbed natural land) or from inputs being substitutes or complements in production or consumption (e.g., nitrogen and phosphorus preferably being used inﬁxed proportions).

The production sectors are modeled either by using an explicit production function or by a production cost function. A production function is speciﬁed for agriculture, energy services, fertilizer production,ﬁsheries, timber production and industrial manufacturing sectors since their factor inputs are directly connected to one or more ESPs (see the previous section on“Economic drivers of planetary pressures”), thus making their input substitutability important. For all sectors except agriculture, we use one level constant elasticity of substitution (CES) functions. For agriculture, we use a nested CES function (see below). Sectors whose production processes are of less importance, are represented by a production cost function. These sectors include phosphate, water, fossil fuel, and renewable energy.

Also, in many sectors, certain inputs e.g., labor and capital, are economically important but their explicit modeling is not directly relevant for our analysis (i.e., of negligible importance to the ESPs). To account for these inputs, we include an aggregate input, which we refer to as other inputs, in all production sectors except energy services and assume that these are supplied with a given sector-speciﬁc price elasticity of supply. The possibility of adjusting these other inputs leads to decreased use in sectors where their marginal value decreases and increased use in sectors where their marginal value increases, and thus to some extent captures the possibility to move inputs between sectors in response to changing economic conditions.

We will now present the model sectors in more detail. A list of model quantities, their prices and uses can be found in Table1(different uses of a quantity are denoted by subscripts).

The agricultural sector uses inputs land (LA), fertilizers (P), water (W), energy services (E_A) and other inputs (MA) as inputs to produce output that can be used for food or biofuels. Producers maximize their proﬁt, taking prices as given. Their proﬁt maximization problem is

LA;P;W;EmaxA;MA

p_AA Lð _A; P; W; EA; MAÞ p_Lc_AðLAÞLA

p_PP p_WW p_EE_A p_M_AM_A; ð1Þ where cA(LA) captures the cost of converting land to agricultural land. The agricultural production function is a CES function between land and non-land inputs, where non-land inputs are aggregated using a CES function.

The energy-services sector combines energy from different sources into a bundle of energy services (E). The different sources are biofuels (AB), fossil fuels (EE) and renewables (R). The producers in this sector solve the proﬁt maximization problem

AmaxB;E_E;Rp_EEðA_B; EE; RÞ pAA_B p_EEE p_RR: ð2Þ We model production of fertilizers (P) as using fossil fuel (EP), phosphate (P) and other inputs (MP). The use of fossil fuel is intended to capture the fossil-fuel (more speciﬁcally natural-gas) intensive production of the nitrogen component of fertilizers. We thus treat fossil fuel use in fertilizer production as a proxy for nitrogen. The proﬁt maximization problem of fertilizer producers is

EPmax;P;MP

p_PP Eð _P; P; MPÞ p_EE_P pPP p_M_PM_P: ð3Þ

For timber production (T) we only consider the input land (LT) and other inputs (MT). The producers then solve the maximization problem

LmaxT;MT

p_TTðL_T; MTÞ p_Lc_TðL_TÞL_T p_M_TM_T; ð4Þ where cTis a cost of converting (e.g., clearing) land for forestry.

Industrial manufacturing (Y) requires energy (E_Y) and other inputs (MY).

While we refer to this sector as manufacturing, the substitutability between energy and other inputs is chosen to match that of the economy as a whole. The substitutability thus reﬂects not only the manufacturing sector but also the service sector that has a signiﬁcantly lower energy intensity but is economically important.

The maximization problem of the representative producer is

max p_YY Eð _Y; MYÞ p_EE_Y p_M_YM_Y: ð5Þ Theﬁsheries sector uses inputs fossil fuel (EF) and other inputs (MF). The producers solve the maximization problem

EmaxF;MF

p_FFðE_F; MFÞ p_EE_F p_M_FM_F: ð6Þ Extraction of fossil fuel (E) is modeled by assuming a gross extraction cost (gE) that increases with increased extraction (gE(E) thus gives the total cost of extracting quantity E). We assume that the tax on fossil fuels (a percentage taxτE) is paid by thefirms that extract and sell it. Extraction firms solve the profit maximization problem

maxE

p_E 1 þτE

E g_EðEÞ: ð7Þ

The sectors phosphate (P), water (W), renewable energy (other than biofuels) (R) and the other inputs (MA, MF, MP, MT, and MY) are similarly represented by a production or extraction cost and the proﬁt-maximization problem of the producers are given by

maxX p_XX g_XðXÞ for X 2 fP; W; R; MA; MF; MP; MT; MYg: ð8Þ We have now described the maximization problems underlying decisions made by all producers. The representative household also solves a maximization problem, maximizing the utility derived from consumption. The households’ preferences are represented by utility function U and the utility-maximization problem, subject to the income being I, is given by

AF;F;Y;LmaxU;T U F A ð _F; FÞ; ~F Y; Lð U; TÞ

s:t: p_AAFþ p_FF þ p_YY þ p_LL_Uþ p_TT≤ I: ð9Þ This speciﬁcation has divided consumption into two levels. While this division is not necessary at this level of generality, it clariﬁes the assumed substitutabilities between goods. We assume greater substitutability within than between categories.

The upper level consists of food (F ) and non-food ( ~F ) goods, with the former category consisting of food from agriculture and fromﬁsheries, and the latter of manufactured goods, natural land and timber. The inclusion of natural land is intended to capture various ways in which households’ demand for natural lands lead to land being kept from other uses, e.g., preservation of land as national parks.

We assume that timber is consumed directly by the households.

This completes the description of the modeling of all decision-making agents in the model. In addition to conditions derived from these maximization problems, we must also specify market-clearing conditions that make sure that supplied and demanded quantities add up.

For land (L), the total supply is assumed to beﬁxed:

L ¼ L_Aþ L_Tþ L_U: ð10Þ

The remaining market-clearing conditions are for agricultural production

A ¼ AFþ A_B; ð11Þ

fossil fuel

E ¼ E_Eþ E_Fþ E_P ð12Þ

and energy services

E ¼ E_Aþ E_Y: ð13Þ

In summary, production functions, market-clearing conditions, budget constraints andﬁrst-order conditions from the maximization problems of representative agents provide us with 41 equilibrium conditions pinning down the 41 endogenous prices and quantities. The full set of equilibrium conditions are available in the Supplementary Methods.

Solution Approach. We note a few features of our model, some of which have already been mentioned: there are no explicit externalities; policies are applied exogenously; all sectors are assumed to be competitive; market clearing determines the equilibrium. In this context, we can work with the decentralized equilibrium, which may be analyzed by considering theﬁrst order conditions. In our model, there are 41 unknown prices and quantities in the model, determined by 41 equilibrium conditions. Being exogenous, policies represent parameters that are Table 1 Model quantities, prices and uses.

Variable Quantity Price Uses

A Agricultural

production

pA Food A_F, biofuels AB

E Fossil fuel pE Energy E_E, Fisheries EFand

fertilizer production EP

E Energy services p_E AgricultureE_A, manufacturing E_Y

F Fisheries pF Food

L Land pL Agriculture LA, timber

production LT, natural land LU

M Other inputs p_M_X MX, for X∈ {A, F, P, T, Y}

P Fertilizers pP Agriculture

P Phosphate p_P Fertilizer production

R Renewables

(excluding biofuels)

pR Energy services

T Timber production pT Consumption

W Fresh water pW Agriculture

Y Manufacturing pY Consumption